Analysis of fracture propagation and shale gas production by intensive volume fracturing

This paper presents an integrated study from fracture propagation modeling to gas flow modeling and a correlation analysis to explore the key controlling factors of intensive volume fracturing.The fracture propagation model takes into account the interaction between hydraulic fracture and natural fracture by means of the displacement discontinuity method(DDM)and the Picard iterative method.The shale gas flow considers multiple transport mechanisms,and the flow in the fracture network is handled by the embedded discrete fracture model(EDFM).A series of numerical simulations are conducted to analyze the effects of the cluster number,stage spacing,stress difference coefficient,and natural fracture distribution on the stimulated fracture area,fractal dimension,and cumulative gas production,and their correlation coefficients are obtained.The results show that the most influential factors to the stimulated fracture area are the stress difference ratio,stage spacing,and natural fracture density,while those to the cumulative gas production are the stress difference ratio,natural fracture density,and cluster number.This indicates that the stress condition dominates the gas production,and employing intensive volume fracturing(by properly increasing the cluster number)is beneficial for improving the final cumulative gas production.

DICE:An open-source MATLAB application for quantification and parametrization of digital outcrop model-based fracture datasets

An open-source MATLAB application(app)named Discontinuity Intensity Calculator and Estimator(DICE)was developed in order to quantitatively characterize the fractures,or in more general,discontinuities within a rocky outcrop in three-dimensional(3D)digital data,such as digital outcrop model(DOM).The workflow proposed for the parametrization of the discontinuities consists of the following steps:(1)Analysis and mapping of the fractures detected within the 3D DOMs;(2)Calculation of the orientation,position and dimensions of discontinuities that are represented by best-fit circular planes;(3)Determining the discontinuity parameters(dimension,distribution,spacing and intensity)by the DICE algorithm using different 3D oriented sampling techniques(3D oriented scanline,3D oriented circular scan window and spherical scan volume).Different sampling methods were bench tested with a synthetic,as well as a natural case study,and compared in order to understand the advantages and limitations of each technique.The 3D oriented circular scan window appears to be the most effective method for fracture intensity estimation with high accuracy(error 0.4%)and stability with variations in scan radius.

SIF-based fracture criterion for interface cracks

The complex stress intensity factor K governing the stress field of an interface crack tip may be split into two parts, i.e.,■ and s^（-iε）, so that K = ■ s^（-iε）, s is a characteristic length and ε is the oscillatory index. ■ has the same dimension as the classical stress intensity factor and characterizes the interface crack tip field. That means a criterion for interface cracks may be formulated directly with■, as Irwin（ASME J. Appl. Mech. 24：361–364, 1957） did in 1957 for the classical fracture mechanics. Then, for an interface crack,it is demonstrated that the quasi Mode I and Mode II tip fields can be defined and distinguished from the coupled mode tip fields. Built upon SIF-based fracture criteria for quasi Mode I and Mode II, the stress intensity factor（SIF）-based fracture criterion for mixed mode interface cracks is proposed and validated against existing experimental results.

Incompatible numerical manifold method for fracture problems

The incompatible numerical manifold method （INMM） is based on the finite cover approximation theory, which provides a unified framework for problems dealing with continuum and discontinuities. The incompatible numerical manifold method employs two cover systems as follows. The mathematical cover system provides the nodes for forming finite covers of the solution domain and the weighted functions, and the physical cover system describes geometry of the domain and the discontinuous surfaces therein. In INMM, the mathematical finite cover approximation theory is used to model cracks that lead to interior discontinuities in the process of displacement. Therefore, the discontinuity is treated mathematically instead of empirically by the existing methods. However, one cover of a node is divided into two irregular sub-covers when the INMM is used to model the discontinuity. As a result, the method sometimes causes numerical errors at the tip of a crack. To improve the precision of the INMM, the analytical solution is used at the tip of a crack, and thus the cover displacement functions are extended with higher precision and computational efficiency. Some numerical examples are given.

A Study on Propagation Mechanism of Fracture Systems in Rock Masses by Discontinuity Displacement Method

The main task of fracture mechanics of rock masses is the study on the propagating mechanism of fractures in rock masses , which can be efficiently conducted by discontinuty displacement (DD) numerical evaluation . Firstly ,the element stress and displacement are analysed and the principle and steps of the numerical calculation of stress intensity factor and fracture extension force are introduced .The numerical results of parallel and echelon fracture systems ,which are compared with real field fractures .are presented. Finally . a simple engineering application example is presented .

Optimization method of fracturing fluid volume intensity for SRV fracturing technique in shale oil reservoir based on forced imbibition:A case study of well X-1 in Biyang Sag of Nanxiang Basin,China

An optimization method of fracturing fluid volume strength was introduced taking well X-1 in Biyang Sag of Nanxiang Basin as an example.The characteristic curves of capillary pressure and relative permeability were obtained from history matching between forced imbibition experimental data and core-scale reservoir simulation results and taken into a large scale reservoir model to mimic the forced imbibition behavior during the well shut-in period after fracturing.The optimization of the stimulated reservoir volume(SRV)fracturing fluid volume strength should meet the requirements of estimated ultimate recovery(EUR),increased oil recovery by forced imbibition and enhancement of formation pressure and the fluid volume strength of fracturing fluid should be controlled around a critical value to avoid either insufficiency of imbibition displacement caused by insufficient fluid amount or increase of costs and potential formation damage caused by excessive fluid amount.Reservoir simulation results showed that SRV fracturing fluid volume strength positively correlated with single-well EUR and an optimal fluid volume strength existed,above which the single-well EUR increase rate kept decreasing.An optimized increase of SRV fracturing fluid volume and shut-in time would effectively increase the formation pressure and enhance well production.Field test results of well X-1 proved the practicality of established optimization method of SRV fracturing fluid volume strength on significant enhancement of shale oil well production.